The point on the y-axis which is equidistant from the point A $(6, 5)$ and B $(- 4, 3)$ is _______________

(0, 7)

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(0, 9)

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(9, 0)

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(0, -9)

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Solution

The correct option is B
(0, 9)

$P A = P B (g i v e n)$

$P A^{2} = P B^{2}$

$(0 - (- 4))^{2} + (y - 3)^{2} = (0 - 6)^{2} + (y - 5)^{2}$

$4^{2} + (y - 3)^{2} = 6^{2} + (y - 5)^{2}$

$/ 16 + / y^{2} - 6 y + / 9 = 36 + / y^{2} - 10 y + / 25$

$4 y = 36$

$y = 9$

$∴ P \equiv (0, 9)$

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